Fast Iterative Integral Equation Solver for Acoustic Scattering by Inhomogeneous Objects Using the Butterfly Approximation.

The acoustic scattering by highly inhomogeneous objects is analyzed by a method-of-moment solver for the volume integral equation. To enable the treatment of acoustically large scatterers of various topologies, the iterative numerical solution of the resulting system is accelerated via a kernel independent algebraic compression scheme: blocks of the hierarchically partitioned moment stiffness matrix are expressed in butterfly form that, for volume problems, scales favorably compared to the popular low-rank approximation. A detailed description of the algorithm, as implemented in this work, is provided.

Manipulation of curved beams using beam-domain optimization.

An efficient scheme for the design of aperture fields (distributed sources) that radiate arbitrary trajectory curved (accelerating) beams, with enhanced controllability of various beam features, is presented. The scheme utilizes a frame-based phase-space representation of aperture fields to overcome the main hurdles in the design for large apertures: First, it uses the a-priory localization of caustic beams to significantly reduce the optimization problem's variable space, to that of few Gaussian window coefficients accurately capturing those beams. Then, the optimization problem is solved in the reduced (local) spectral domain.

Fast Computation of Born-Approximated Multistatic Scattering.

An algorithm for the fast computation of multistatic scattering patterns, produced by low-contrast inhomogeneous volumetric objects, which satisfy the Born approximation assumption, is presented. The algorithm relies on hierarchical interpolation and aggregation of optimally sampled phase-compensated partial contributions to the scattered field integral. The Born approximation enables the efficient simultaneous computation for ranges of incident and observation angles, as well as excitation frequencies.

Manipulation and control of 3-D caustic beams over an arbitrary trajectory.

We present an algorithm for manipulating and controlling 3-D field patterns, with energy confined to the narrow vicinity of predefined 3-D trajectories in free-space, which are of arbitrary curvature and torsion. This is done by setting the aperture field's phase to form smooth caustic surfaces that include the desired trajectory. The aperture amplitude distribution is constructed to manipulate both the on-axis intensity profile and the off-axis beam-width, and is updated iteratively.

A fast and stable solver for acoustic scattering problems based on the nonuniform grid approach.

A fast and stable boundary element method (BEM) algorithm for solving external problems of acoustic scattering by impenetrable bodies is developed. The method employs the Burton-Miller integral equation, which provides stable convergence of iterative solvers, and a generalized multilevel nonuniform grid (MLNG) algorithm for fast evaluation of field integrals. The MLNG approach is used here for the removal of computational bottlenecks involved with repeated matrix-vector multiplications as well as for the low-order basis function regularization of the hyper-singular integral kernel.

Fast direct solution of 3-D scattering problems via nonuniform grid-based matrix compression.

A fast non-iterative algorithm for the solution of large 3-D acoustic scattering problems is presented. The proposed approach can be used in conjunction with the conventional boundary element discretization of the integral equations of acoustic scattering. The algorithm involves domain decomposition and uses the nonuniform grid (NG) approach for the initial compression of the interactions between each subdomain and the rest of the scatterer.

Multilevel nonuniform grid algorithm for acceleration of integral equation-based solvers for acoustic scattering.

A fast algorithm for the evaluation of acoustic fields produced by given source distributions is developed with the aim of accelerating iterative boundary element method (BEM) solvers. The algorithm is based on field smoothing by phase and amplitude compensation, which allows for sampling of the fields radiated by finite-size source distributions over coarse nonuniform (spherical) grids (NGs). Subsequently, the fields at the desired target points can be obtained by an interpolation and phase and amplitude restoration.